Nonparametric analysis Kruskal-Wallis test

For the sake of this example, we use the data from the parametric ANOVA example to illustrate the Kruskal-Wallis test. If it seems at all strange to use the same data for both examples, a parametric analysis and a nonparametric analysis, it is worth noting that a nonparametric analysis is always appropriate for a given dataset meeting the requirements at the start of the chapter. Parametric analyses are not always appropriate for all datasets. 

The post-intervention data were not distributed in a way that allowed transformation to normality. No information was collected on subjects that had been sampled multiple times, so it was not possible to account for this in analysis. Medians were reported and nonparametric Wilcoxon and Kruskal—Wallis tests were used to examine group differences, and the Spearman rank procedure for the analysis of correlations. 

The analysis of rank data, what is generally called nonparametric statistical analysis, is an exact parallel of the more traditional (and familiar) parametric methods. There are methods for the single comparison case (just as Student s t-test is used) and for the multiple comparison case (just as analysis of variance is used) with appropriate post hoc tests for exact identification of the significance with a set of groups. Four tests are presented for evaluating statistical significance in rank data the Wilcoxon Rank Sum Test, distribution-free multiple comparisons, Mann-Whitney U Test, and the Kruskall-Wallis nonparametric analysis of variance. For each of these tests, tables of distribution values for the evaluations of results can be found in any of a number of reference volumes (Gad, 1998). 

Data were expressed as the mean standard error of the mean (SEM). Differences between means were determined using one-way analysis of variance (ANOVA) followed by the Tukey-Kramer post hoc comparison and two-sided t test. For comparing percentages, nonparametric tests were also applied (Mann-Whitney, Kruskal-Wallis). Differences were considered significant when p < 0.05. 

Fig. 26.6 The time between contact and the cradle-carrying behavior in male shore crabs (red or green color morphs) exposed to copper chloride (CuCl2) (0.1 or 0.5 mg L 1 Cu) and in control males. The male stands guard over the female and this guarding behavior is induced by pheromones in the female urine. Kruskal-Wallis nonparametric variance analysis followed by Mann Whitney U-test, demonstrated that the latency between contact and cradle-carrying was longer in copper exposed male compare to the unexposed controls (figure from Krang and Ekerholm 2006 photo by K. Reise). Figure reprinted with permission from Elsevier...

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